Velocity Calculator

Speed is how fast you are moving (a scalar). Velocity is speed in a stated direction (a vector). This calculator works with the one-dimensional case along a straight line, so a positive value means motion one way and a negative value means motion the opposite way. When all four formulas reduce to a single number on a number line, the magnitude is the speed and the sign is the direction.

Use distance / time when an object moves at a roughly constant speed and you know how far it went and how long it took. Use v = u + a*t when you know how fast the object started, how hard it accelerated, and for how long. Use v^2 = u^2 + 2*a*s when you know how far it accelerated instead of how long. Use the average form (u + v) / 2 when you only have the starting and ending speeds and the acceleration was constant: that average equals the time-weighted mean velocity exactly for uniform acceleration.

Because the discriminant u^2 + 2*a*s can be negative. That happens when you decelerate (negative a) over more distance than the object actually has energy to cover. For example, an object moving at 10 m/s decelerating at 2 m/s^2 stops after 25 m, so asking for its velocity at 30 m has no real answer. The calculator returns null in that case rather than pretending the motion continues.

Mach 1 is the local speed of sound, which varies mainly with temperature and gas composition. The calculator uses a fixed 343 m/s reference, approximately the speed of sound in dry air near 20 degrees C. It is not the International Standard Atmosphere sea-level value at 15 degrees C, and it should not replace local atmospheric data for flight calculations.

One g is 9.80665 m/s^2, the CGPM standard gravitational acceleration. Pick g from the acceleration unit dropdown and enter values like 0.5 (half a g, gentle braking), 1 (free-fall), or 6 (a fighter jet pulling out of a dive). The calculator multiplies your number by 9.80665 before plugging it into v = u + a*t or v^2 = u^2 + 2*a*s, so you can think in human-scale g-units without doing the conversion yourself.